1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
miv72 [106K]
3 years ago
9

What is the fifth term of the sequence whose first term is 10 and whose common ratio is 1/2?

Mathematics
2 answers:
Cloud [144]3 years ago
8 0

Answer:

D


Step-by-step explanation:

Common ratio of half means that to get each successive terms, you have to multiply the preceding term by half.

Since first term is 10

2nd term is 10*\frac{1}{2}=5

3rd term is 5*\frac{1}{2}=\frac{5}{2}

4th term is \frac{5}{2}*\frac{1}{2}=\frac{5}{4}

5th term is \frac{5}{4}*\frac{1}{2}=\frac{5}{8}


Answer choice D is right.

Kipish [7]3 years ago
3 0

The fifth term of the sequence whose first term is 10 and whose common ratio is ½ is 5/8. The correct answer between all the choices given is the last choice or letter D. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

You might be interested in
The summer monsoon brings 80% of India's rainfall and is essential for the country's agriculture.
Natasha_Volkova [10]

Answer:

Step 1. Between 688 and 1016mm. Step 2. Less than 688mm.

Step-by-step explanation:

The <em>68-95-99.7 rule </em>roughly states that in a <em>normal distribution</em> 68%, 95% and 99.7% of the values lie within one, two and three standard deviation(s) around the mean. The z-scores <em>represent values from the mean</em> in a <em>standard normal distribution</em>, and they are transformed values from which we can obtain any probability for any normal distribution. This transformation is as follows:

\\ z = \frac{x - \mu}{\sigma} (1)

\\ \mu\;is\;the\;population\;mean

\\ \sigma\;is\;the\;population\;standard\;deviation

And <em>x</em> is any value which can be transformed to a z-value.

Then, z = 1 and z = -1 represent values for <em>one standard deviation</em> above and below the mean, respectively; values of z = 2 and z =-2, represent values for two standard deviations above and below the mean, respectively and so on.

Because of the 68-95-99.7 rule, we know that approximately 95% of the values for a normal distribution lie between z = -2 and z = 2, that is, two standard deviations below and above the mean as remarked before.

<h3>Step 1: Between what values do the monsoon rains fall in 95% of all years?</h3>

Having all this information above and using equation (1):

\\ z = \frac{x - \mu}{\sigma}  

For z = -2:

\\ -2 = \frac{x - 852}{82}

\\ -2*82 + 852 = x

\\ x_{below} = 688mm

For z = 2:

\\ 2 = \frac{x - 852}{82}

\\ 2*82 = x - 852

\\ 2*82 + 852 = x

\\ x_{above} = 1016mm

Thus, the values for the monsoon rains fall between 688mm and 1016mm for approximately 95% of all years.

<h3>Step 2: How small are the monsoon rains in the driest 2.5% of all years?</h3>

The <em>driest of all years</em> means those with small monsoon rains compare to those with high values for precipitations. The smallest values are below the mean and at the left part of the normal distribution.

As you can see, in the previous question we found that about 95% of the values are between 688mm and 1016mm. The rest of the values represent 5% of the total area of the normal distribution. But, since the normal distribution is <em>symmetrical</em>, one half of the 5% (2.5%) of the remaining values are below the mean, and the other half of the 5% (2.5%) of the remaining values are above the mean. Those represent the smallest 2.5% and the greatest 2.5% values for the normally distributed data corresponding to the monsoon rains.

As a consequence, the value <em>x </em>for the smallest 2.5% of the data is precisely the same at z = -2 (a distance of two standard deviations from the mean), since the symmetry of the normal distribution permits that from the remaining 5%, half of them lie below the mean and the other half above the mean (as we explained in the previous paragraph). We already know that this value is <em>x</em> = 688mm and the smallest monsoons rains of all year are <em>less than this value of x = </em><em>688mm</em>, representing the smallest 2.5% of values of the normally distributed data.

The graph below shows these values. The shaded area are 95% of the values, and below 688mm lie the 2.5% of the smallest values.

3 0
3 years ago
A 4 metre ladder is placed against a vertical wall.
Black_prince [1.1K]

Answer:

Original position: base is 1.5 meters away from the wall and the vertical distance from the top end to the ground let it be y and length of the ladder be L.

Step-by-step explanation:

By pythagorean theorem, L^2=y^2+(1.5)^2=y^2+2.25 Eq1.

Final position: base is 2 meters away, and the vertical distance from top end to the ground is y - 0.25 because it falls down the wall 0.25 meters and length of the ladder is also L.

By pythagorean theorem, L^2=(y -0.25)^2+(2)^2=y^2–0.5y+ 0.0625+4=y^2–0.5y+4.0625 Eq 2.

Equating both Eq 1 and Eq 2: y^2+2.25=y^2–0.5y+4.0625

y^2-y^2+0.5y+2.25–4.0625=0

0.5y- 1.8125=0

0.5y=1.8125

y=1.8125/0.5= 3.625

Using Eq 1: L^2=(3.625)^2+2.25=15.390625, L=(15.390625)^1/2= 3.92 meters length of ladder

Using Eq 2: L^2=(3.625)^2–0.5(3.625)+4.0625

L^2=13.140625–0.90625+4.0615=15.390625

L= (15.390625)^1/2= 3.92 meters length of ladder

<em>hope it helps...</em>

<em>correct me if I'm wrong...</em>

4 0
3 years ago
What is the inverse of the function shown( in the form of a graph)
NemiM [27]

Answer:

y =  - 1x + b

Step-by-step explanation:

The inverse of a slope is the exact opposite slope of the original. I'll show a function below where you can easily solve future problems if you need to.

-  \frac{1}{m} x

m is the slope, so for the equation above, you simply insert the original slope, being 1, in the equation.

-  \frac{1}{1} x \\  - 1x

So the inverse slope would be -1.

6 0
3 years ago
Please give me the answer
Tcecarenko [31]

Answer:

7 units

Step-by-step explanation:

hope I helped today

8 0
3 years ago
Read 2 more answers
What's X?<br><img src="https://tex.z-dn.net/?f=%20-%203x%20-%2010%20%3D%205" id="TexFormula1" title=" - 3x - 10 = 5" alt=" - 3x
Dmitry [639]

-3x - 10 =5

-3x = 15

x = -5


2x + 6 = -8

2x = -14

x = -7


5 0
3 years ago
Other questions:
  • Asaad originally practices on a rectangular football field with and area of 2x2 square yards.
    15·1 answer
  • −3x^ 4−7x+17=0
    14·1 answer
  • Find the area of the parallelogram that has a base of 2 1/2 feet and a height of 1 1/4 feet
    10·1 answer
  • WILL REWARD THE BRAINLIEST
    13·2 answers
  • Find the equation of the line that passes through the point left (-9,12) and is perpendicular to the line y=3/2x-1/2. Write the
    12·1 answer
  • Can the absolute value of -4 be 1/4
    5·2 answers
  • AABC is similar to AAXY by a ratio of 4:3. If BC = 24, what is the length of XY?
    15·1 answer
  • Which expression is equivalent to -15x + 39?
    7·2 answers
  • If d - 10. r<br> PLZ HELP ASAP I ONLY HAVE A MIN
    11·1 answer
  • What is the solution of the system? Use elimination. 5x = -30 + 5y 20y = 105 + 5x 0 (-1,4) D5, 20) KO (-1, 5) (5.-1)​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!